An enhancement of the finite element method using Kriging interpolation (K-FEM)
has been recently proposed and applied to solve one- and two- dimensional linear elasticity
problems. The key advantage of this innovative method is that the polynomial refinement can be
performed without adding nodes or changing the element connectivity. This paper presents the
development of the K-FEM for static and free vibration analyses of Timoshenko beams. The
transverse displacement and the rotation of the beam are independently approximated using
Kriging interpolation. For each element, the interpolation function is constructed from a set of
nodes within a prescribed domain of influence comprising the element and its several layers of
neighbouring elements. In an attempt to eliminate the shear locking, the selective-reduced
integration technique is utilized. The developed beam element is tested to several static and free
vibration problems. The results demonstrate the excellent performance of the developed element.